Sally is a frequent flyer whose fares are reduced through coupon offerings. She receives a 20% reduction on fares after she flies 20,000 miles, and 40% reduction after she flies 40,000 miles.
a) Illustrate her budget constraint.
b) Illustrate how her level of utility will change given these frequent-flyer coupons.

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I am very confused by this question. Here we are asked to find the budget constraint, but I am not even sure what the two goods are...what are the goods that should be plotted on the vertical and horizontal axes? Will the budget line be a straight line? How would the coupons change the budget line?

Ok, Put air-line travel miles on the x-axis, "all other goods" on the y-axis. On the x-axis, mark a point for 20000 miles, and another at 40000.

Begin high up on the on the y-axis and start drawing a standard budget constraint line. However, when the line hits the 20000 level, the price of travel suddenly drops. This is represented as a kink on the budget line; Sally can get more airline miles than a straight-line budget constraint would show. Continue the new budget constraint line from the kink point until you hit 40000, in which you get another kink point. Continue from here until you eventually hit the x-axis.

Pat yourself on the back.

b) Utility maximization will still occur when the highest indifference curve is tangent to the 3-part budget constraint line. It will be theoretically possible that a single indifference curve could be tangent at 2 or even all 3 parts of the constraint.

Between 20k and 40k miles, slope (in absolute value) of budget line is p1/1=p1
Between 20k and 40k miles, slope (in absolute value) of budget line is 0.8p1/1=0.8p1.
More than 40k miles, slope (in absolute value) of budget line is ??? Is it just 0.6p1?

b) For this part, the question asks how her level of utility will CHANGE given these frequent-flyer coupons. I don't quite understand it.
How it will CHANGE relative to what? My best guess is that it is asking us to compare the budget line in part a with the straight budget line that has a slope of p1 everywhere (i.e. for the case in which there is no flyer coupons).
I think it is trying to ask whether her utility will be better off, worse off, or the same. But we aren't even told what her utility maximizing points are, how can we answer this question?

Thank you very much!

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